A137596 - OEIS

%I #22 Mar 07 2025 07:45:29

%S 1,1,1,1,2,1,1,3,4,1,1,4,11,7,1,1,5,26,32,11,1,1,6,57,122,76,16,1,1,7,

%T 120,423,426,156,22,1,1,8,247,1389,2127,1206,288,29,1,1,9,502,4414,

%U 9897,8157,2934,491,37,1

%N Triangle read by rows: T(n, k) = Sum_{i=0..n) Stirling2(i, k).

%F T = A000012 * A048993 as infinite lower triangular matrices.

%F T(n, k) = Sum_{i=0..n-k} Stirling2(i+k, k). - _Igor Victorovich Statsenko_, May 25 2024

%e First few rows of the triangle:

%e   1;

%e   1, 1;

%e   1, 2,   1;

%e   1, 3,   4,   1;

%e   1, 4,  11,   7,   1;

%e   1, 5,  26,  32,  11,   1;

%e   1, 6,  57, 122,  76,  16,  1;

%e   1, 7, 120, 423, 426, 156, 22, 1;

%e   ...

%p T := (n, k) -> add(Stirling2(i, k), i=0..n):

%p seq(seq(T(n, k), k=0..n), n=0..9);  # _Peter Luschny_, Mar 07 2025

%Y Cf. A005001 (row sums), A048993.

%K nonn,tabl,changed

%O 0,5

%A _Gary W. Adamson_, Jan 29 2008

%E Offset set to 0 by _Peter Luschny_, May 25 2024